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Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes
Author(s) -
Tsai Henghsiu,
Chan K. S.
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00422.x
Subject(s) - mathematics , maximum likelihood sequence estimation , estimator , maximum likelihood , statistics , estimation theory , likelihood function , restricted maximum likelihood , consistent estimator , efficient estimator , minimum variance unbiased estimator
Tsai and Chan (2003) has recently introduced the Continuous‐time Auto‐Regressive Fractionally Integrated Moving‐Average (CARFIMA) models useful for studying long‐memory data. We consider the estimation of the CARFIMA models with discrete‐time data by maximizing the Whittle likelihood. We show that the quasi‐maximum likelihood estimator is asymptotically normal and efficient. Finite‐sample properties of the quasi‐maximum likelihood estimator and those of the exact maximum likelihood estimator are compared by simulations. Simulations suggest that for finite samples, the quasi‐maximum likelihood estimator of the Hurst parameter is less biased but more variable than the exact maximum likelihood estimator. We illustrate the method with a real application.